Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
vector<int> vec;
int main() {
  int n;
  cin >> n;
  vec.push_back(0);
  for (int i = 1; i <= n; i++) {
    vec.push_back(i + vec[i - 1]);
    if ((i + vec[i - 1]) >= n) break;
  }
  int flag = 0;
  for (int i = 1; i < vec.size(); i++) {
    if (binary_search(vec.begin() + 1, vec.end(), n - vec[i])) {
      flag = 1;
      break;
    }
  }
  if (flag == 1 && n != 1)
    cout << "YES\n";
  else
    cout << "NO\n";
  return 0;
}